Lesson topic: Decimal number system.

Lesson type: a lesson in “discovering” new knowledge.

Equipment: board, interactive whiteboard, projector, flashcards, presentation.

Lesson objectives:

· Educational: introducing students to the textbook, introducing the concept of a natural number.

· Educational: develop the ability to analyze, compare, generalize, draw conclusions, develop attention, develop oral speech.

· Educational: cultivate the ability to express one’s point of view, listen to the answers of others, take part in dialogue, and develop the ability for positive cooperation.

Methods:

By sources of knowledge: verbal, visual;

According to the degree of teacher-student interaction: heuristic conversation; interactive method.

Regarding didactic tasks: preparation for perception;

Regarding the nature of cognitive activity: active method, reproductive, partially search.

Planned result.

UUD.

Personal: ability for self-assessment based on the criterion of success in educational activities.

Subject: understand what a “natural number” is, “classes of natural numbers”; be able to correctly read natural numbers and correlate classes with each other.

Metasubject:

regulatory - be able to determine and formulate a goal in a lesson with the help of a teacher; pronounce the sequence of actions in the lesson; work according to a collectively drawn up plan; evaluate the correctness of the action at the level of an adequate retrospective assessment; plan your action in accordance with the task; make necessary adjustments to the action after its completion based on its evaluation and taking into account the nature of the errors made; express your guess; record individual difficulties in a trial learning activity;

communicative - be able to express your thoughts with sufficient completeness and accuracy; express your thoughts orally and in writing; listen and understand the speech of others; jointly agree on the rules of behavior and communication at school and follow them; argue your opinion and position;

cognitive - be able to navigate your knowledge system (distinguish what is new from what is already known with the help of a teacher); gain new knowledge (find answers to questions using the textbook, your life experience and information received in class); structure knowledge; use sign-symbolic means

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Technological map of the lesson.

Lesson topic : Decimal number system.

Lesson type : a lesson in “discovering” new knowledge.

Equipment: board, interactive whiteboard, projector, flashcards, presentation.

Lesson objectives:

• Educational: introducing students to the textbook, introducing the concept of a natural number.
• Educational: develop the ability to analyze, compare, generalize, draw conclusions, develop attention, develop oral speech.
• Educational: cultivate the ability to express one’s point of view, listen to the answers of others, take part in dialogue, and develop the ability for positive cooperation.

Methods:

By sources of knowledge: verbal, visual;

According to the degree of teacher-student interaction: heuristic conversation; interactive method.

Regarding didactic tasks: preparation for perception;

Regarding the nature of cognitive activity: active method, reproductive, partially search.

Planned result.

UUD.

Personal: ability for self-assessment based on the criterion of success in educational activities.

Subject: understand what a “natural number” is, “classes of natural numbers”; be able to correctly read natural numbers and correlate classes with each other.

Metasubject:

regulatory - be able to determine and formulate a goal in a lesson with the help of a teacher; pronounce the sequence of actions in the lesson; work according to a collectively drawn up plan; evaluate the correctness of the action at the level of an adequate retrospective assessment; plan your action in accordance with the task; make necessary adjustments to the action after its completion based on its evaluation and taking into account the nature of the errors made; express your guess; record individual difficulties in a trial learning activity;

communicative -be able to express your thoughts with sufficient completeness and accuracy; express your thoughts orally and in writing; listen and understand the speech of others; jointly agree on the rules of behavior and communication at school and follow them; argue your opinion and position;

educational - be able to navigate your knowledge system (distinguish new from already known with the help of a teacher); gain new knowledge (find answers to questions using the textbook, your life experience and information received in class); structure knowledge; use sign-symbolic means

Technological map of a mathematics lesson in 5th grade using a textbook

Mathematics. 5th grade.Muravin G.K., Muravin O.V.

« Decimal number system».

Stage lesson.	Stage tasks.	Teacher's activities.	Student activities.	Time.	Formed UUD
1.Organizational stage.	Meet the students. Introduce the children to the textbook. Create a favorable psychological mood for work.	The lesson begins with the teacher introducing himself to the students. The teacher introduces himself to the students and says a few words about himself. The teacher has a badge attached to his chest, on which the teacher’s first, middle and last names are written. The teacher hands out name tags to the students and asks them to write their first name in the form in which they want to be addressed and their last name. Teacher: “You are offered a list of goals for studying mathematics. Mark the goals that are most important to you. After filling out the form, you must submit it.” The teacher introduces the textbook and its structure. Students should pay attention to the section of the textbook “Answers, tips, solutions”, open the list of additional literature, and also look at Chapter 6 “Repetition”. Each point of the chapter “Repetition” begins with historical material, which can be used both for studying the material of the main points and for the final repetition. Summarizes this stage of the lesson. It is necessary to emphasize that the study of mathematics in the 5th grade begins with the repetition and systematization of material studied in elementary school, which enables students to be successful from the very first lessons. At the same time, students must understand that a lot of new and interesting things await them in 5th grade.	They sign badges and stick them on their chests Slide 2. Students read the questionnaire and ask questions if they don’t understand something. Fill out the form. Students become familiar with the endpapers of the textbook. They are looking for known material that they studied in elementary school, and unknown material that they will study in 5th grade. Students read the table of contents of the textbook and read the chapter titles. Students see that in the first chapter there is a lot of material that is already familiar to them, but the names of other chapters and paragraphs are unfamiliar to them.		Communicative: Planning educational collaboration with the teacher and peers. Regulatory: organization of your educational activities. Personal: motivation for learning.
2. Setting the goals and objectives of the lesson. Motivation for students' learning activities.	Providing motivation for children to learn and their acceptance of lesson goals.	WITH how many stars are there in the sky? And a blade of grass in the field? How many crumbs are there in the bread? How many drops are there in the sea? There is no answer to these questions, But now, children, I'll give you one piece of advice. If you try to be friends with numbers, You don't have to be afraid Live and not bother. Do not be afraid that you will offend your friends, Count and see: Simple, no fuss, and candy and toys, Dolls, books and firecrackers can be divided equally, Don't forget anyone. You will overcome all sciences. The guys will say about you: “Our friend is a crazy person.” And when the years pass, You will be an adult then. Maybe you will become an astronaut, you can reach the heavens with your hand. So as not to get bored during the flight, you can count the stars. V. N. Savichev What is the poem talking about? (About numbers.) How many numbers are there? What can you write down using numbers? Write down 3 numbers in your notebooks. Read them. What do you think we will study in class today? Today we will get acquainted with the new topic “Natural Numbers”, we will learn how to denote natural numbers, write them and read numbers correctly	Slide 3. Teachers listen They answer the question. Write down the date in the notebook, determine the topic and goals of the lesson.		Communicative: be able to jointly agree on the rules of behavior and communication, follow them, and express their thoughts orally.
3. Updating knowledge	Updating basic knowledge and methods of action.	Organization of mental calculation, repetition of the multiplication table. We will repeat the multiplication table using this table. Find the letters corresponding to the numbers. Write these letters in your notebook and read the resulting statement about mathematics.	Complete the task Slide 4.		Cognitive: generating interest in this topic. Regulatory: control and evaluation of the process and results of activities.
4. Primary assimilation of new knowledge.	Ensuring the perception, comprehension and primary memorization of knowledge and methods of action, connections and relationships in the object of study	What are the names of the numbers that we used when repeating the multiplication table? Shows demonstration material from the electronic supplement to the textbook by G. K. Muravina, O. V. Muravina “Mathematics. 5th grade"	The teachers are listening. Watching the presentation. Make notes in a notebook.		Cognitive: be able to navigate your knowledge system (distinguish new from what is already known with the help of a teacher, structure knowledge, transform information from one form to another). Communicative: be able to listen and understand the speech of others, express thoughts orally and in writing, argue your opinion and position. Regulatory: be able to express one's guess, record individual difficulties in a trial learning activity.
5. Initial check of understanding		Gives a task from the textbook Working with the textbook: With. 7, no. 2 After receiving the answer, discusses with students why some statements are true and others are not. Working with the textbook: With. 7, no. 4	Slide 5. Students complete No. 2 independently and make up a number from the numbers of the correct statements. Take part in the discussion. Perform No. 4 frontally (using signal cards.		Subject: Be able to write natural numbers and read the notation of numbers. Cognitive: be able to acquire new knowledge (find answers to questions using a textbook, your life experience and information received in class).Communicative:be able to express your thoughts orally, listen and understand the speech of others. Regulatory: evaluate the correctness of actions at the level of adequate assessment
6. Primary consolidation.	Establishing the correctness and awareness of mastering new educational material; identifying gaps and misconceptions and correcting them.	What are natural numbers used for? What is the smallest natural number? What do we use to write natural numbers? How many digits do we use to write any natural number? Is zero considered a natural number?	Slide 6. Answer questions in your notebook.		Personal: formation of positive self-esteem, learn to accept the reasons for success (failure). Communicative: plan cooperation, use criteria to justify their judgments. Regulatory: the ability to independently adequately analyze the correctness of actions and make the necessary adjustments.
7. Reflection (summarizing the lesson)	Give a quantitative assessment of student work.	Summarize the work of the pairs and the class as a whole. Organize the discussion: What was the topic of the lesson? If you think that you understand the topic of the lesson, then glue a green piece of paper. If you think that you have not understood the topic enough, then stick a yellow piece of paper. If you think that you did not understand the topic of the lesson, then stick a red piece of paper.	Slide 7. Students summarize their work: I realized today... I learned today... I like it…, I did not like. I didn't understand…		Regulatory: assessment of one's own activities in the classroom.
8. Information about homework, instructions on how to complete it	Ensuring that children understand the content and methods of completing homework.	Gives comments on homework. Page 7, No. 3, p. 13 No. 25*, 26*.	Slide 8. Students write down the assignment in their diaries.

List of used literature:

1. Mathematics. Grade 5: technological maps of lessons based on the textbook by N. Ya. Vilenkin, M34 by V. I. Zhokhov, A. S. Chesnokov, S. I. Shvartsburd. I half of the year / author.-comp. I. B. Chaplygina. - Volgograd: Teacher, 2014. - 228 p.
2. Mathematics. 5th grade: method. Study guide. G.K. Mupavina, O.V. Muravina “Mathematics. 5th grade." At 2 p.m. Part 1/ G.K. Muravin, O.V. Muravina. – M.: Bustard, 2012. – 174 p.

Lesson summary on the topic:

« Number systems»

Completed by: computer science teacher

Yarovenko S.S.

Grade: 8

Lesson topic: Number systems.

Lesson type: learning new material.

Lesson objectives:

Introduce students to the history of the emergence and development of number systems.

Point out the main disadvantages of non-positional number systems.

To develop in students the concept of “positional number systems”

Requirements for knowledge and skills:

Students should know:

Definition of the following concepts: “digit”, “number”, “number system”, “non-positional number system”;

Disadvantages of non-positional number systems;

Which number system is called “positional” and why;

Give examples of positional number systems;

Expanded form of writing a number in the positional number system.

Students should be able to:

Write numbers in non-positional number systems;

Give examples of numbers of different positional number systems, determine the base of the number system;

Be able to write numbers of the positional number system in expanded form.

Software: Microsoft PowerPoint program,

presentation "Number systems".

Lesson Plan

Types and forms of work

Time

1. Org. moment

Greetings

0.5 min

2. Presentation of new material

The teacher presents the material, while simultaneously demonstrating the presentation of “Number Systems”. The tasks proposed in the presentation are completed.

25 min

3. Consolidation of the material covered.

Working with the textbook

10 min

4. Summing up

Grading

2 minutes

5. Lesson reflection

1 min

7. Homework

1.5 min

During the classes

Organizing time

Presentation of new material

The presentation of new material is accompanied by a presentation. "Number systems". Presentation is attached.

1. History of the emergence and development of number systems

(Slides 1-4)

People have always counted and written down numbers. But they were written down completely differently, according to different rules. However, in any case, the number was depicted using some symbols called numbers.

Question: What are numbers? (Students try to answer this question). Numbers- these are the symbols involved in writing a number and making up some alphabet.

Question: What is a number?

Initially, the number was tied to those items that were counted. But with the advent of writing, number was separated from objects of counting and the concept of a natural number appeared. Fractional numbers appeared due to the fact that a person needed to measure something, and the unit of measurement did not always fit an integer number of times in the measured value. Further, the concept of number developed in mathematics, and today it is considered a fundamental concept not only of mathematics, but also of computer science. Number is a certain quantity.

Numbers are made up of digits according to special rules. At different stages of human development, among different peoples, these rules were different, and today we call them number systems.

1. Number systems.

Notation is a way of writing numbers using digits.

(Slide 5)

All known number systems are divided into non-positional and positional.

Non-positional number systems arose earlier than positional ones. A non-positional number system is a number system in which the quantitative equivalent (“weight”) of a digit does not depend on its location in the number record. Positional number systems, in which the quantitative equivalent (“weight”) of a digit depends on its location in the number record.

Let's look at examples of writing numbers in positional and non-positional number systems.

The number is 333. This number is written using the digit 3 three times. But the contribution of each digit to the value of the number is different. The first 3 means the number of hundreds, the second - the number of tens, the third - the number of units. If we compare the “weight” of each digit in this number, it turns out that the first 3 is “more” than the second by 10 times and “more” by the third by 100 times.

This principle is absent in non-positional number systems. Consider the Roman numeral XXX. In the decimal number system, this number is 30. When writing the number XXX, the same “digits” were used - X. And if we compare them with each other, we get absolute equality. Those. No matter what place a digit appears in a number, its “weight” is always the same. In this example it is 10.

1. Non-positional number systems

(Slide 6)

In ancient times, when people began to count, there was a need to write down numbers. The number of objects, for example bags, was depicted by drawing dashes or serifs on any hard surface: stone, clay, wood (the invention of paper was still very far away). Each bag in such a record corresponded to one line.

Scientists called this method of writing numbers the unit or unary number system.

The inconveniences of such a number system are obvious: the larger the number you need to write, the more sticks there are. When writing down a large number, it is easy to make a mistake - add an extra number of sticks or, conversely, not add enough sticks. Therefore, later these icons began to be combined into groups of 3, 5, 10 sticks. Thus, more convenient number systems arose.

(Slide 7)

The ancient Egyptian decimal non-positional system arose in the second half of the third millennium BC. The paper was replaced by a clay tablet, and that is why the numbers have such an outline.

In this number system, the key numbers 1, 10, 100, 1000, etc. were used as digits. and they were written using special hieroglyphs: pole, arc, rolled palm leaf, lotus flower.

It was from combinations of such “digits” that numbers were written and each “digit” was repeated no more than nine times.

Question: Why? (Students try to answer this question).

Answer: Since ten consecutive identical digits can be replaced by one number, but one digit higher.

All other numbers were compiled from these key numbers using ordinary addition.

Question: What number is written down? (Students try to answer this question).

Answer : 2342

(Slide 8)

The Roman system we know is not fundamentally different from the Egyptian one. But it is more common these days.

It uses the signs I (one finger) for the number 1, V (open palm) for the number 5, X (two folded palms) for 10, and for the numbers 50, 100, 500 and 1000, capital letters of the corresponding Latin letters are used to denote numbers. words

I, V, X, L, C, D and M are the "digits" of this number system. A number in the Roman numeral system is designated by a set of consecutive “digits”.

Rules for composing numbers in the Roman numeral system: The size of a number is determined as the sum or difference of the digits in the number. If the smaller number is to the left of the larger one, then it is subtracted. If the smaller number is to the right of the larger one, then it is added.

(Slide 9)

Let's look at how the number 444 is written in the Roman numeral system.

444 = 400+40+4 (the sum of four hundreds, four tens and four ones).

400 = D - C = CD, 40 = L - X = XL, 4 = V - I = IV

444 = CDXLIV

Please note that the decimal number system uses three identical digits, while the Roman number system uses different numbers. The number of digits used to write the same number is not the same in the decimal and Roman systems (twice as much in the Roman system).

(Slide 10)

Question: What numbers are written using Roman numerals?

MMIV = 1000 + 1000 + (5 – 1) = 2004

LXV = 50 + 10 + 5 = 65

CMLXIV = (1000 – 100) + 50 + 10 + (5 – 1) = 964

Question: Follow the steps.

MMMD + LX = (1000 + 1000 + 1000 + 500) + (50 + 10) = 3560

Question: While performing this arithmetic operation, did you experience any inconvenience, and what was it? (Students try to answer this question).

(Slide 12)

The Greeks used several ways to write numbers. The Athenians used the first letters of numerals to denote numbers. Using these numbers, a resident of Ancient Greece could write down any number.

Question: Try to determine what number is written in the Greek number system? (Students try to answer this question).

(Slide 13)

Alphabetic systems were more advanced non-positional number systems. Such number systems included Slavic, Ionian (Greek), Phoenician and others. In them, numbers from 1 to 9, whole numbers of tens (from 10 to 90), and whole numbers of hundreds (from 100 to 900) were designated by letters of the alphabet.

The alphabetic system was also adopted in ancient Rus'. Until the end of the 17th century (before the reform of Peter I), 27 Cyrillic letters were used as “numbers”.

To distinguish letters from numbers, a special sign was placed above the letters - a title. This was done in order to distinguish numbers from ordinary words.

Question : What number is written in the Slavic number system? (Students try to answer this question).

We see that the entry is no longer than our decimal. This is because alphabetic systems used at least 27 "digits". But these systems were only convenient for recording numbers up to 1000.

(Slide 14)

True, the Slavs, like the Greeks, knew how to write down numbers greater than 1000. To do this, new designations were added to the alphabetic system.

So, for example, the numbers 1000, 2000, 3000... were written in the same “digits” as 1, 2, 3..., only a special sign was placed in front of the “digit” at the bottom left.

The number 10,000 was denoted by the same letter as 1, only without a title, it was circled. This number was called “darkness”. This is where the expression “darkness to the people” comes from.

Question: What number in the Slavic number system corresponds to the expression “darkness of darkness”? (Students try to answer this question).

Answer: 100 000 000.

This method of writing numbers, as in the alphabetic system, can be considered as the beginnings of a positional system, since in it the same symbols were used to designate units of different digits, to which only special signs were added to determine the value of the digit.

Alphabetic number systems were not very suitable for handling large numbers. When writing a large number for which there was no sign to designate it, there was a need to maintain a new symbol to designate this number.

During the development of human society, these systems gave way to positional systems.

(Slide 15)

Question: Remember which number system (positional or non-positional) uses more digits when writing a number, and which number system (positional or non-positional) is more convenient to perform arithmetic operations. And answer the question: What are the disadvantages of non-positional number systems? (Students try to answer this question).

1. Positional number systems

(Slide 16)

Due to the above-mentioned disadvantages, non-positional number systems gradually gave way to positional number systems.

The main advantages of the positional number system:

Ease of performing arithmetic operations.

A limited number of characters required to write a number.

(Slide 17)

Discharge is the position of the digit in the number.

The base (basis) of the positional number system is the number of digits or other signs used to write numbers in a given number system.

There are many positional systems, since any number not less than 2 can be taken as the base of the number system.

Data on some number systems are given in the table.

(Slide 18)

In the positional number system, any real number can be represented as:

A q = ±(a n-1 q n-1 +a n-2 q n-2 +…a 0 q 0 +a -1 q -1 +a -2 q -2 +…a -m q -m)

Here:

A – the number itself

q – base of the number system

a i – digits of a given number system

n – number of digits of the integer part of the number

m – number of digits of the fractional part of the number

Let's imagine the decimal number A = 4718.63 in expanded form.

In what number system is the number written?

What is the base of this number system? (q =10)

What is the number of digits of the integer part of the number (n = 4)

What is the number of digits of the fractional part of a number (m = 2)

(Slide 19)

Question: What will the number A 8 = 7764.1 look like when expanded? (Students try to answer this question).

(Slide 20)

Question: What will the number A 16 = 3AF look like when expanded? (Students try to answer this question).

(Slide 21)

The collapsed form of writing a number is called writing in the form:

A = a n-1 a n-2 … a 1 a 0 , a -1 a -m

This is the form of writing numbers that we use in everyday life.

III. Consolidating new material

Complete tasks:

№1

What number is written using Roman numerals: MCMLXXXVI?

№2

Follow these steps:

MCMXL+LX

№3

Are the numbers written correctly in the corresponding number systems?

A 10 = A.234 B) A 16 = 456.46

A 8 = -5678 D) A 2 = 22.2

№4

Completing textbook tasks 1-5 p. 48.

IV. Summarizing

The teacher evaluates the work of the class and names the students who excelled in the lesson.

V. Lesson reflection.

Questions for students:

- What new did you learn in class today?

What new concepts did you become familiar with?

What tasks did you find difficult to complete?

VI. Homework assignment

Lesson #1

Subject: Decimal number system

The date of the:

Target: repeat the features of constructing the decimal number system, the names of the digits.

Tasks:- give the concept of the decimal number system;

Develop logical thinking and attention

Cultivate accuracy, hard work, perseverance

During the classes:

Organizational moment

Oral exercises

a) Arrange the order of the actions and insert the numbers in the “boxes”.

45:5+39:13+85:17+48:16=

b) Write down and continue the next two rows:

90 dec., 91 dec., …., 99 dec., 100 dec.

900, 910, ….., 990, 1000

3. Preparation for work at the main stage of the lesson

Let's remember the name of the digits of the number.

How to find out how many are in tens? ( You need to close the units digit and read the remaining numbers. It will represent the number of tens).

Write down any numbers that have 2 hundreds. ( 200, 201, 234, etc.).

- Increase any of these numbers by 4 hundred. ( 201+400=601)

- How many hundreds are in this number? ( 6 hundreds)

- How many hundreds will we get if we increase the number 934 by 1 hundred? ( 934+100=1034; 10 hundreds and 34 more).

Read these numbers, highlighting the tens: 234 – 23 dec., 932 – 93 dec., 975 – 97 dec., 1000 – 100 dec.

Read these numbers, highlighting hundreds: 234 - 2 hundred, 932 - 9 hundred, etc.

№1 (p.4)

Read the numbers held by the forest school students. (594, 451, 275). How many hundreds, tens and ones are there in each number? (594 – 5 hundred, 9 des., 4 units, etc.)

In which notation does the number 5 represent the number of hundreds? (594)

What about the number of tens and units? (451, 275)

Helper card

Rank

Hundreds

Dozens

Units

! The same digit in a number can have different meanings depending on what digit it is in. When writing a number, the value of the digit increases 10 times from digit to digit (from units to hundreds). Therefore, the system of notation of numbers that we use is called the decimal number system.

Physical education minute – visual gymnastics

№2 p.5(No. 1 p. 4)

67 – 6 des., 7 units, 290 – 2 hundred, 9 des., 0 – units. etc.

№3 p.5(No. 2 p. 4)

Write numbers using numerals. ( 448, 905, 950, 200 )

5. Repetition of previously covered material

№11 p.7 (No. 10 p.6)

Difference in example: 80:2 and 84:2

№12 s. 7(On the desk)

How are the expressions similar and different? Calculate.

48:6+26∙2= 60 (48:6+26) ∙2 = 68

Physical education minute

№13 p.7(- from the words of the teacher)

760-60:4=645 17∙5-38=47

52:4∙5=90 (120+60):90=2

№15 (1.2) s. 8. (- On the desk)

38∙x, if x=10 409+y, if y = 302

38∙10 = 380 409+302= 711

38∙x, if x= 8 409+y, if y = 501

38∙8 = 304 409+501 = 910

38∙x, if x=5 409+y, if y = 511

38∙5=190 409+511 = 920

6. Lesson summary:

What is the name of the number system we use? Why is it called that?

7. Home exercise:

Uch. rule c. 5(p.4) learned, R.t. With. 3 No. 1, p.4

Lesson #2

Subject: Decimal number system

The date of the:

Target: repeat the features of constructing the decimal number system, the names of the digits; teach to represent numbers as a sum of digit terms.

Tasks:- learn to represent numbers as a sum of digit terms

During the classes:

1.Org.moment

2. Oral exercises ( in warehouses )

a) Find the extra expression. On what basis?

b) How many rectangles are shown?

3. Checking homework

What did we talk about in the last lesson? What is the decimal number system and why is it called that?

4. Assimilation of new knowledge and methods of action

Today we will continue to work with the decimal number system.

How many hundreds, tens and ones are in the number 836? It can be written as a sum.

836= 8∙100+3∙10+6

Each term of the sum is called a digit term, and the number 836 is represented as a sum of digit terms.

№4 p.5(No. 3 p. 5)

327=3∙100+2∙10+7 318 =3∙100+1∙10+8

418 = 4∙100+1∙10+8, etc. 727= 7∙100+2∙10+7, etc.

№ 5 s. 5(No. 4 p. 5)

Write the meaning of the expression in numbers.

692, 130, 18, 705

№ 6 p. 6(No. 5 p. 5)

(805, 850, 508, 580)

(855, 858, 885, 805,558, 850, 888, 588, 585, 580, 508, 555)

Physical education minute

5. Repetition of previously covered material

№16 p. 8(No. 11 p.6)

It was – 85 l

Topped up - ? l

Now - 192 l

Solution:

107 (l) – topped up

Answer: 107 liters were added.

№ 17 p.8(- slide)

price

Lined up

the same

9 – 5 = 4 (t.) – more in a line

Answer: more lined notebooks, paid more for lined notebooks.

№ 18 p. 8(slide)

price

Lined up

the same

T. for 4 b.

Rub for 12 rubles.

12: 4 = 3 (r.) – price of notebook

Answer: The price of a notebook is 3 rubles.

№19 p.8(- slide)

price

Lined up

the same

Rub for 12 rubles.

9-5=4 (t.) – cost 12 rubles.

12:4=3 (rub.) – price

9∙3 = 27 (rub.) – costs 9 tetras.

5∙3 = 15 (rub.) – costs 5 tetras.

Answer: lined 27 RUR, checkered 15 RUR.

6. Lesson summary

What can any number be represented as? (as a sum of bit terms)

7. Homework

Uch. With. Rule 5, R.t. With. 3, 5

Lesson objectives:

Educational:

define the concept of “number system”;

derive an algorithm for converting numbers from binary to decimal and vice versa;

learn to convert numbers from the decimal number system to the arbitrary number system.

Educational:

education of information culture, attention, accuracy, perseverance.

Educational:

development of the ability to highlight the main thing (when compiling a lesson summary);

development of self-control (analysis of self-control of mastering educational material according to the sheet);

development of cognitive interests (use of gaming techniques in the classroom).

Lesson plan:

Organizing time.

Explaining new material and performing the practical part of the lesson.

Summing up the lesson.

Homework.

During the classes

1. Organizational moment.

Announcing the topic and objectives of the lesson. Designation of the lesson plan.

In order to move on to studying the decimal and binary number systems, let's figure out what number systems are and where they come from. Presentation “Number systems. Historical sketch" ( ).

Let's start studying the topic of today's lesson with one, at first glance, incomprehensible and confusing poem (Slide 19 of the presentation).

She was a thousand and one hundred years old
She went to the hundred and first grade,
She carried a hundred books in her briefcase -This is all true, not nonsense.
When, dusting with a dozen feet,
She walked along the road
The puppy was always running after her
With one tail, but one hundred-legged.
She caught every sound
With your ten ears,And ten tanned hands
They held the briefcase and leash.
And ten dark blue eyesWe looked at the world as usual,But everything will become completely normal,When you understand our story.

In order to understand what the author wanted to tell us, we need to study the topic “Binary and decimal number systems.” So, as you may have guessed, today's topic islesson "Binary and decimal number systems."

2. Explanation of new material and implementation of the practical part of the lesson.

Theoretical material:

Notation is an accepted way of recording numbers and comparing these records with real values. All number systems can be divided into two classes:

positional - the quantitative value of each digit depends on its location (position) in the number;

non-positional - numbers do not change their quantitative value when their position in the number changes.

To record numbers in different number systems, a certain number of characters or digits are used. The number of such signs in the positional number system is callednumber system base .

Base

Each number in the positional number system can be represented as a sum of products of coefficients by the power of the base of the number system.

For example:

from left to right, starting from "0" )

Now let's look at the algorithm for converting numbers from an arbitrary number system to decimal using the example.

Algorithm for converting numbers from an arbitrary number system to decimal:

(we place powers over the integer part of the numberfrom left to right , over the fractional part –from right to left, starting from "-1" )

The binary number system is of particular importance in computer science. This is determined by the fact that the internal representation of any information in a computer is binary, that is, described by sets of only two characters (0, 1).

Let's look at an example of number translationfrom decimal to binary:

Picture 1

Explanation: The solution is written on the board by the teacher with a clear explanation of each action.

The result wasis a number made up of remainders from division by 2 (which we circled), written from right to left.

342 10 = 101010110 2

Now try to write down the considered algorithm for converting a number from the decimal number system in words (for completing the taskI am allotted 2-3 minutes, the teacher controls its implementation). After the allotted time, the teacher asks several students to read the algorithm they have compiled. Then the rest of the students, under the guidance of the teacher, adjust the algorithm. The teacher formulates an algorithm, students write it down in their workbooks.

Algorithm for converting decimal numbers to the binary number system:

Divide the number by 2. Record the remainder (0 or 1) and the quotient.

If the quotient is not equal to 0, then divide it by 2, and so on until the quotient becomes equal to 0. If the quotient is equal to 0, then write down all the resulting remainders, starting from the first, from right to left.

Now we know how to convert numbers from the decimal number system to binary and how to convert numbers from an arbitrary number system to ddecimal Let's solve a few examples (one student goes to the board, the rest complete the task in a notebook and check the result on the board).

Exercise:

Convert numbers to decimal number system: 101111001 2 ,1231 3 , 110110101 2 , 1223 3 .

Convert numbers from decimal to binary and vice versa: 256, 457, 845, 1073.

Write down an algorithm for converting a number from the decimal number system to an arbitrary number system.

Explanation: The task is completed at the board by students assigned by the teacher.

In order to consolidate the knowledge and skills acquired in today's lesson, let's play a little. Exercise"build by points" . To complete this task, you will need not only the knowledge gained in today's lesson, but also mathematical knowledge.

Each studenta notebook sheet with a coordinate system printed on it is issued (prepared in advance by the teacher) – .

Explanation of the task: each point coordinate is written in a binary systememe coordinates. You need to convert the coordinates of the points into the decimal number system and, using knowledge of mathematics, construct points on the coordinate system and connect them. Points of one object are designated by one letter.

Head:

G1 (101;1011)

G2 (1100;1011)

G3 (101;100)

G4 (1100;100)

Neck:

Ш1 (111;100)

Ш2 (1010;100)

Ш3 (1010;11)

Ш4 (111;11)

Eyes:

Ch1 (110;1010)

Ch2 (1000;1010)

Ch3 (1000;1000)

Ch4 (110;1000)

Ch5 (1001;1010)

Ch6 (1011;1010)

Ch7 (1011;1000)

Ch8 (1001;1000)

Nose:

H1 (1000;111)

H2 (1001;111)

Mouth:

P1 (110;110)

P2 (110;101)

P3 (1011;101)

P4 (1011;110)

Antennas:

A1 (110;1011)

A2 (110;1111)

A3 (101;1111)

A4 (111;1111)

A5 (1011;1011)

A6 (1011;1111)

A7 (1010;1111)

A8 (1100;1111)

As a result, you should get a portrait of a ROBOT you know well.

Figure 2

Students have been familiar with the image of a robot since the 7th grade: it is an assistant who helps in performing practical work and in studying graphic design.Paint editors learned how to create a picture using the appliqué method and drew a portrait of a robot.

3. Summing up the lesson.

Students fill out a cardSelf-analysis of students’ mastery of educational material and hand it over to the teacher ( ) .

Checking the completion of the task (“drawing by dots”).

Frontal survey:

what is a number system;

define the concept of “base of number system”;

how to convert a number from the decimal number system to binary (algorithm).

Grading for the lesson.

4. Homework.

Now let's go back to the beginning of the lesson and remember the poem that we did not understand.

Note: The teacher hands out a printout to the students.poems ( ).

Homework: Reword the poem using what you learned in class.

Lesson #1

Subject: Decimal number system

The date of the:

Target: repeat the features of constructing the decimal number system, the names of the digits.

Tasks: - give the concept of the decimal number system;

Develop logical thinking and attention

Cultivate accuracy, hard work, perseverance

During the classes:

1. Organizational moment
2. Oral exercises

a) Arrange the order of the actions and insert the numbers in the “boxes”.

45:5+39:13+85:17+48:16=

b) Write down and continue the next two rows:

90 dec., 91 dec., …., 99 dec., 100 dec.

900, 910, ….., 990, 1000

3. Preparation for work at the main stage of the lesson

Let's remember the name of the digits of the number.

How to find out how many are in tens? (You need to close the units digit and read the remaining numbers. It will represent the number of tens).

Write down any numbers that have 2 hundreds. ( 200, 201, 234, etc.).

- Increase any of these numbers by 4 hundred. ( 201+400=601)

- How many hundreds are in this number? ( 6 hundreds)

- How many hundreds will we get if we increase the number 934 by 1 hundred? (934+100=1034; 10 hundreds and 34 more).

Read these numbers, highlighting the tens: 234 – 23 dec., 932 – 93 dec., 975 – 97 dec., 1000 – 100 dec.

Read these numbers, highlighting hundreds: 234 - 2 hundred, 932 - 9 hundred, etc.

No. 1 (p. 4)

Read the numbers held by the forest school students. (594, 451, 275). How many hundreds, tens and ones are there in each number? (594 – 5 hundred, 9 des., 4 units, etc.)

In which notation does the number 5 represent the number of hundreds? (594)

What about the number of tens and units? (451, 275)

Helper card

Rank
Hundreds	Dozens	Units

! The same digit in a number can have different meanings depending on what digit it is in. When writing a number, the value of the digit increases 10 times from digit to digit (from units to hundreds). Therefore, the system of notation of numbers that we use is called the decimal number system.

Physical education minute –visual gymnastics

No. 2 p.5 (No. 1 p. 4)

67 – 6 des., 7 units, 290 – 2 hundred, 9 des., 0 – units. etc.

No.3 p.5 (No.2 p.4)

Write numbers using numerals. ( 448, 905, 950, 200 )

5. Repetition of previously covered material

No. 11 p. 7 (No. 10 p. 6)

Difference in example: 80:2 and 84:2

No. 12 p. 7 (on the board)

How are the expressions similar and different? Calculate.

48:6+26∙2= 60 (48:6+26) ∙2 = 68

Physical education minute

№13 p.7 (- from the words of the teacher)

760-60:4=645 17∙5-38=47

52:4∙5=90 (120+60):90=2

No. 15 (1,2) p. 8 . (- On the desk)

38∙x, if x=10 409+y, if y = 302

38∙10 = 380 409+302= 711

38∙x, if x= 8 409+y, if y = 501

38∙8 = 304 409+501 = 910

38∙x, if x=5 409+y, if y = 511

38∙5=190 409+511 = 920

6. Lesson summary:

What is the name of the number writing system we use? Why is it called that?

7. Home exercise :

Uch. rule c. 5(p.4) learned, R.t. With. 3 No. 1, p.4

Lesson #2

Subject: Decimal number system

The date of the:

Target: repeat the features of constructing the decimal number system, the names of the digits; teach to represent numbers as a sum of digit terms.

Tasks: - learn to represent numbers as a sum of digit terms

During the classes:

1.Org.moment

2. Oral exercises ( in warehouses)

a) Find the extra expression. On what basis?

b) How many rectangles are shown?

3. Checking homework

What did we talk about in the last lesson? What is the decimal number system and why is it called that?

4. Assimilation of new knowledge and methods of action

Today we will continue to work with the decimal number system.

How many hundreds, tens and ones are in the number 836? It can be written as a sum.

836= 8∙100+3∙10+6

Each term of the sum is called a digit term, and the number 836 is represented as a sum of digit terms.

No.4 p.5 (No.3 p.5)

327=3∙100+2∙10+7 318 =3∙100+1∙10+8

418 = 4∙100+1∙10+8, etc. 727= 7∙100+2∙10+7, etc.

No. 5 p. 5 (No. 4 p. 5)

Write the meaning of the expression in numbers.

692, 130, 18, 705

No. 6 p. 6 (No. 5 p. 5)

(805, 850, 508, 580)

(855, 858, 885, 805,558, 850, 888, 588, 585, 580, 508, 555)

Physical education minute

5. Repetition of previously covered material

No. 16 p. 8 (No. 11 p.6)

It was – 85 l

Topped up - ? l

Now - 192 l

Solution:

107 (l) – topped up

Answer: 107 liters were added.

No. 17 p.8 (- slide)

Solution:

1. 9 – 5 = 4 (t.) – more in a line

Answer: more lined notebooks, paid more for lined notebooks.